You should be able to cast to multiple CC from one computer (not simultaneously). All cast devices will be listed in the "Cast button" pull-down menu (you need to first setup each CC from chromecast app).

* Once cast devices are (setup &) connected to the network, they should be listed in the "Cast button" pull-down menu in any (supported) computer(s)/ phone(s)/ tablet(s) that is connected to the same network.

same issue here. 6 TVs, 6 ChromeCasts. The idea was to assign one tab to each TV, but it doesn't work that way. Doesn't look like this is supported. One solution proposed was running 6 virtual machines but that would just be a pain to administer. Back to the drawing board.

We tried the virtual machine approach with VirtualBox and it works at home, but here in the office it does not (it's probably something to do with the security setup in our office wireless network).
In a nutshell, the virtual machines, despite having a bridged network, do not get a unique IP and therefore cannot cast to an alternate chromecast.
We're still playing around with VirtualBox to get it to work on our office network, but so far, no luck.

This may not be a solution, but it's a workaround I've been using. I have 3 chromecasts, 3 TV's, and one computer.

in chrome, it is possible to create different users thought the settings menu in the upper right corner. For each chromecast I have, I've created a new user in chrome with the same name (living room, office, & master bedroom). I then open three different chrome windows on my desktop, and switch each window to a different user via the settings menu. Now, each window is working independently, and can cast to separate chromecasts simultaneously.

Theres difficulty working with full screen, but at least this is close.